No, I have not had actual experience of this. The outcome would depend on the jurisdiction and the legislation. I've added a case study from a book that I wrote a couple of years ago and while the circumstances are not the same as yours, the outcome may not go your way.
Case study 2.6: McDonnell v Harrison (2012) NSWLEC 1291
Facts
Sandra McDonnell and Edward and Sarah Harrison were next-door neighbours
in Sydney. Mrs McDonnell had serious concerns about the damage that was
being done to her property by a 12-metre high jacaranda tree, a three-metre
high lillypilly and two five-metre high palm trees that grew on the Harrisons’
property.
Mrs McDonnell was concerned that the trees had damaged her property and had
made an application in terms of the Trees (Disputes Between Neighbours Act)
2006 (NSW), seeking both orders for removal of each of the trees and orders for
compensation for past damage caused by some of them. Mrs McDonnell engaged
a consultant to investigate the trees and the damage for a fee of $100.
The alleged damage to Mrs McDonnell’s property included a deck that had rotted
and had to be demolished, requiring the re-laying of pavers. There was also
distortion of the boundary fence due to the intrusion of the jacaranda’s roots.
Each of the trees also dropped leaf litter and fruit on Mrs McDonnell’s property.
Issues
Should the court make orders for the Harrisons to remove the trees and pay
compensation to Mrs McDonnell for damage caused?
Decision
Senior Commissioner Tim Moore and Commissioner Judy Fakes took into
consideration the Act as well as some relevant decisions of earlier cases in the
Land and Environment Court. The case of Barker v Kyriakides (2007) NSWLEC
292 was relevant to material dropped by trees. The court ruled that there was
nothing in this case to require that the trees be removed or that compensation
should be made for the normal dropping of leaf litter. The case of Yang v Scerri
(2007) NSWLEC 592 provided guidance in the area of future damage. The court
concluded that there was no basis either on damage or likely future damage
that would be caused by the trees.
The court dismissed the application for the removal of the trees. In terms of
the distortion to the fence, the court ruled that the aesthetic benefits of the
tree outweighed any damage.
The court considered that the $100 fee paid by Mrs McDonnell was a reasonable
cost incurred in investigating the issues. The court ordered that the Harrisons
reimburse Mrs McDonnell for the sum within 14 days of the hearing.
Source: www.caselaw.nsw.gov.au/action/PJUDG?s=1000,jgmtid=161371